Identifying Power Functions

Which of the following functions are power functions?

$$\begin{aligned}f \left(x\right) & = & 1 & \text{Constant}\textrm{ }\text{function} \\ f \left(x\right) & = & x & \text{Identity}\textrm{ }\text{function} \\ f \left(x\right) & = & x^{2} & \text{Quadratic}\textrm{ }\text{function} \\ f \left(x\right) & = & x^{3} & \text{Cubic}\textrm{ }\text{function} \\ f \left(x\right) & = & \frac{1}{x} & \text{Reciprocal}\textrm{ }\text{function} \\ f \left(x\right) & = & \frac{1}{x^{2}} & \text{Reciprocal}\textrm{ }\text{squared}\textrm{ }\text{function} \\ f \left(x\right) & = & \sqrt{x} & \text{Square}\textrm{ }\text{root}\textrm{ }\text{function} \\ f \left(x\right) & = & \sqrt[3]{x} & \text{Cube}\textrm{ }\text{root}\textrm{ }\text{function}\end{aligned}$$